#define MATHTOOLS_CPP
#define CORE_DLL
/***************************************************************\

    ^^^^^^^^  ^^^^^^^^  ^^^^^^^^  ^^^^^^^^
    ^^    ^^  ^^    ^^     ^^     ^^    ^^
    ^^        ^^^^^^^^     ^^     ^^^^^^^^
    ^^   ^^^  ^^    ^^     ^^     ^^    ^^
    ^^    ^^  ^^    ^^     ^^     ^^    ^^
    ^^^^^^^^  ^^    ^^  ^^^^^^^^  ^^    ^^

    sample code from the book...
    Real Time 3D Terrain Engines Using C++ and DirectX

    by Greg Snook
    greg@mightystudios.com

\***************************************************************/
#include "core\core.h"
#include "math_tools.h"
#include "windows.h"


using namespace gaia;


const float gaia::FLOAT_PRECISION					= (float)(3.4e-8);
const float gaia::PI								= (float)(3.14159265358979323846264338327950288419716939937511);
const float gaia::TWO_PI							= (float)(2.0*PI);
const float gaia::HALF_PI							= (float)(PI/2.0);
const float gaia::QUARTER_PI						= (float)(PI/4.0);
const float gaia::EIGHTH_PI						= (float)(PI/8.0);
const float gaia::PI_SQUARED						= (float)(9.86960440108935861883449099987615113531369940724079);
const float gaia::PI_INVERSE						= (float)(0.31830988618379067153776752674502872406891929148091);
const float gaia::PI_OVER_180						= (float)(PI/180);
const float gaia::PI_DIV_180						= (float)(180/PI);
const float gaia::NATURAL_LOGARITHM_BASE			= (float)(2.71828182845904523536028747135266249775724709369996);
const float gaia::EULERS_CONSTANT					= (float)(0.57721566490153286060651);
const float gaia::SQUARE_ROOT_2					= (float)(1.41421356237309504880168872420969807856967187537695);
const float gaia::INVERSE_ROOT_2					= (float)(0.707106781186547524400844362105198);
const float gaia::SQUARE_ROOT_3					= (float)(1.73205080756887729352744634150587236694280525381038);
const float gaia::SQUARE_ROOT_5					= (float)(2.23606797749978969640917366873127623544061835961153);
const float gaia::SQUARE_ROOT_10					= (float)(3.16227766016837933199889354443271853371955513932522);
const float gaia::CUBE_ROOT_2						= (float)(1.25992104989487316476721060727822835057025146470151);
const float gaia::CUBE_ROOT_3						= (float)(1.44224957030740838232163831078010958839186925349935);
const float gaia::FOURTH_ROOT_2					= (float)(1.18920711500272106671749997056047591529297209246382);
const float gaia::NATURAL_LOG_2					= (float)(0.69314718055994530941723212145817656807550013436026);
const float gaia::NATURAL_LOG_3					= (float)(1.09861228866810969139524523692252570464749055782275);
const float gaia::NATURAL_LOG_10					= (float)(2.30258509299404568401799145468436420760110148862877);
const float gaia::NATURAL_LOG_PI					= (float)(1.14472988584940017414342735135305871164729481291531);
const float gaia::BASE_TEN_LOG_PI					= (float)(0.49714987269413385435126828829089887365167832438044);
const float gaia::NATURAL_LOGARITHM_BASE_INVERSE	= (float)(0.36787944117144232159552377016146086744581113103177);
const float gaia::NATURAL_LOGARITHM_BASE_SQUARED	= (float)(7.38905609893065022723042746057500781318031557055185);
const float gaia::GOLDEN_RATIO						= (float)((SQUARE_ROOT_5 + 1.0) / 2.0);
const float gaia::DEGREE_RATIO						= (float)(PI_DIV_180);
const float gaia::RADIAN_RATIO						= (float)(PI_OVER_180);
const float gaia::GRAVITY_CONSTANT					= 9.81f;


float gaia::s_SinCosTable[TRIG_TABLE_SIZE]=
{
 0.00000000f, 0.00306796f, 0.00613588f, 0.00920376f, 0.01227154f, 0.01533921f, 0.01840673f, 0.02147408f, 0.02454123f, 0.02760815f, 0.03067480f, 0.03374117f, 0.03680722f, 0.03987293f, 0.04293826f, 0.04600319f,
 0.04906768f, 0.05213170f, 0.05519525f, 0.05825827f, 0.06132074f, 0.06438264f, 0.06744392f, 0.07050458f, 0.07356457f, 0.07662386f, 0.07968244f, 0.08274027f, 0.08579732f, 0.08885355f, 0.09190896f, 0.09496350f,
 0.09801714f, 0.10106987f, 0.10412164f, 0.10717243f, 0.11022221f, 0.11327095f, 0.11631864f, 0.11936522f, 0.12241068f, 0.12545499f, 0.12849811f, 0.13154003f, 0.13458072f, 0.13762012f, 0.14065824f, 0.14369504f,
 0.14673048f, 0.14976454f, 0.15279719f, 0.15582840f, 0.15885815f, 0.16188639f, 0.16491312f, 0.16793831f, 0.17096189f, 0.17398387f, 0.17700422f, 0.18002291f, 0.18303989f, 0.18605515f, 0.18906868f, 0.19208041f,
 0.19509032f, 0.19809842f, 0.20110464f, 0.20410897f, 0.20711139f, 0.21011184f, 0.21311033f, 0.21610680f, 0.21910125f, 0.22209363f, 0.22508392f, 0.22807209f, 0.23105812f, 0.23404196f, 0.23702361f, 0.24000303f,
 0.24298018f, 0.24595505f, 0.24892761f, 0.25189781f, 0.25486568f, 0.25783110f, 0.26079413f, 0.26375470f, 0.26671275f, 0.26966834f, 0.27262136f, 0.27557182f, 0.27851969f, 0.28146493f, 0.28440756f, 0.28734747f,
 0.29028469f, 0.29321918f, 0.29615089f, 0.29907984f, 0.30200595f, 0.30492923f, 0.30784965f, 0.31076717f, 0.31368175f, 0.31659338f, 0.31950203f, 0.32240769f, 0.32531029f, 0.32820985f, 0.33110631f, 0.33399966f,
 0.33688986f, 0.33977690f, 0.34266073f, 0.34554133f, 0.34841868f, 0.35129276f, 0.35416353f, 0.35703096f, 0.35989505f, 0.36275575f, 0.36561301f, 0.36846685f, 0.37131721f, 0.37416407f, 0.37700742f, 0.37984723f,
 0.38268346f, 0.38551608f, 0.38834506f, 0.39117038f, 0.39399204f, 0.39681000f, 0.39962420f, 0.40243465f, 0.40524131f, 0.40804416f, 0.41084319f, 0.41363832f, 0.41642958f, 0.41921690f, 0.42200029f, 0.42477968f,
 0.42755511f, 0.43032649f, 0.43309382f, 0.43585709f, 0.43861625f, 0.44137129f, 0.44412217f, 0.44686884f, 0.44961134f, 0.45234960f, 0.45508361f, 0.45781332f, 0.46053872f, 0.46325979f, 0.46597651f, 0.46868885f,
 0.47139674f, 0.47410023f, 0.47679925f, 0.47949377f, 0.48218378f, 0.48486927f, 0.48755017f, 0.49022651f, 0.49289820f, 0.49556527f, 0.49822769f, 0.50088537f, 0.50353837f, 0.50618666f, 0.50883013f, 0.51146889f,
 0.51410276f, 0.51673180f, 0.51935601f, 0.52197528f, 0.52458972f, 0.52719915f, 0.52980363f, 0.53240311f, 0.53499764f, 0.53758711f, 0.54017150f, 0.54275078f, 0.54532498f, 0.54789406f, 0.55045801f, 0.55301672f,
 0.55557024f, 0.55811852f, 0.56066161f, 0.56319934f, 0.56573182f, 0.56825894f, 0.57078075f, 0.57329720f, 0.57580823f, 0.57831383f, 0.58081394f, 0.58330870f, 0.58579785f, 0.58828157f, 0.59075969f, 0.59323233f,
 0.59569931f, 0.59816074f, 0.60061651f, 0.60306662f, 0.60551107f, 0.60794979f, 0.61038280f, 0.61281008f, 0.61523163f, 0.61764735f, 0.62005723f, 0.62246132f, 0.62485951f, 0.62725180f, 0.62963825f, 0.63201874f,
 0.63439327f, 0.63676190f, 0.63912445f, 0.64148104f, 0.64383155f, 0.64617604f, 0.64851439f, 0.65084672f, 0.65317285f, 0.65549284f, 0.65780669f, 0.66011435f, 0.66241580f, 0.66471100f, 0.66699994f, 0.66928262f,
 0.67155898f, 0.67382902f, 0.67609274f, 0.67835003f, 0.68060100f, 0.68284553f, 0.68508369f, 0.68731534f, 0.68954057f, 0.69175929f, 0.69397146f, 0.69617712f, 0.69837624f, 0.70056880f, 0.70275474f, 0.70493412f,
 0.70710677f, 0.70927286f, 0.71143222f, 0.71358490f, 0.71573085f, 0.71787006f, 0.72000253f, 0.72212821f, 0.72424710f, 0.72635919f, 0.72846442f, 0.73056281f, 0.73265427f, 0.73473889f, 0.73681659f, 0.73888737f,
 0.74095112f, 0.74300796f, 0.74505782f, 0.74710065f, 0.74913639f, 0.75116515f, 0.75318682f, 0.75520140f, 0.75720888f, 0.75920922f, 0.76120239f, 0.76318842f, 0.76516730f, 0.76713890f, 0.76910335f, 0.77106053f,
 0.77301049f, 0.77495313f, 0.77688849f, 0.77881652f, 0.78073722f, 0.78265059f, 0.78455663f, 0.78645521f, 0.78834647f, 0.79023021f, 0.79210657f, 0.79397547f, 0.79583693f, 0.79769087f, 0.79953730f, 0.80137616f,
 0.80320758f, 0.80503136f, 0.80684757f, 0.80865622f, 0.81045723f, 0.81225061f, 0.81403637f, 0.81581444f, 0.81758481f, 0.81934756f, 0.82110256f, 0.82284981f, 0.82458931f, 0.82632107f, 0.82804507f, 0.82976127f,
 0.83146966f, 0.83317018f, 0.83486289f, 0.83654773f, 0.83822471f, 0.83989382f, 0.84155500f, 0.84320825f, 0.84485358f, 0.84649098f, 0.84812033f, 0.84974176f, 0.85135520f, 0.85296065f, 0.85455799f, 0.85614735f,
 0.85772860f, 0.85930181f, 0.86086696f, 0.86242396f, 0.86397284f, 0.86551362f, 0.86704624f, 0.86857074f, 0.87008703f, 0.87159508f, 0.87309498f, 0.87458664f, 0.87607008f, 0.87754530f, 0.87901223f, 0.88047093f,
 0.88192129f, 0.88336337f, 0.88479710f, 0.88622254f, 0.88763964f, 0.88904840f, 0.89044875f, 0.89184070f, 0.89322430f, 0.89459950f, 0.89596629f, 0.89732462f, 0.89867449f, 0.90001589f, 0.90134889f, 0.90267330f,
 0.90398932f, 0.90529674f, 0.90659571f, 0.90788615f, 0.90916800f, 0.91044128f, 0.91170603f, 0.91296220f, 0.91420978f, 0.91544873f, 0.91667908f, 0.91790080f, 0.91911387f, 0.92031831f, 0.92151403f, 0.92270112f,
 0.92387956f, 0.92504925f, 0.92621028f, 0.92736256f, 0.92850608f, 0.92964089f, 0.93076700f, 0.93188429f, 0.93299282f, 0.93409258f, 0.93518353f, 0.93626571f, 0.93733901f, 0.93840355f, 0.93945926f, 0.94050610f,
 0.94154406f, 0.94257319f, 0.94359344f, 0.94460487f, 0.94560736f, 0.94660091f, 0.94758558f, 0.94856137f, 0.94952822f, 0.95048606f, 0.95143503f, 0.95237499f, 0.95330608f, 0.95422810f, 0.95514119f, 0.95604527f,
 0.95694035f, 0.95782644f, 0.95870346f, 0.95957154f, 0.96043050f, 0.96128052f, 0.96212143f, 0.96295327f, 0.96377605f, 0.96458977f, 0.96539444f, 0.96619004f, 0.96697646f, 0.96775383f, 0.96852213f, 0.96928126f,
 0.97003126f, 0.97077215f, 0.97150391f, 0.97222650f, 0.97293997f, 0.97364426f, 0.97433937f, 0.97502536f, 0.97570217f, 0.97636974f, 0.97702813f, 0.97767735f, 0.97831738f, 0.97894818f, 0.97956979f, 0.98018217f,
 0.98078531f, 0.98137921f, 0.98196387f, 0.98253930f, 0.98310548f, 0.98366243f, 0.98421007f, 0.98474848f, 0.98527765f, 0.98579752f, 0.98630810f, 0.98680943f, 0.98730141f, 0.98778415f, 0.98825759f, 0.98872167f,
 0.98917651f, 0.98962200f, 0.99005824f, 0.99048507f, 0.99090266f, 0.99131089f, 0.99170977f, 0.99209934f, 0.99247956f, 0.99285042f, 0.99321193f, 0.99356413f, 0.99390697f, 0.99424046f, 0.99456459f, 0.99487931f,
 0.99518472f, 0.99548078f, 0.99576741f, 0.99604470f, 0.99631262f, 0.99657112f, 0.99682033f, 0.99706006f, 0.99729043f, 0.99751145f, 0.99772304f, 0.99792528f, 0.99811810f, 0.99830157f, 0.99847561f, 0.99864024f,
 0.99879545f, 0.99894130f, 0.99907774f, 0.99920475f, 0.99932241f, 0.99943060f, 0.99952942f, 0.99961883f, 0.99969882f, 0.99976939f, 0.99983060f, 0.99988234f, 0.99992472f, 0.99995762f, 0.99998116f, 0.99999529f,
 1.00000000f, 0.99999529f, 0.99998116f, 0.99995762f, 0.99992472f, 0.99988234f, 0.99983060f, 0.99976939f, 0.99969882f, 0.99961883f, 0.99952942f, 0.99943060f, 0.99932235f, 0.99920475f, 0.99907774f, 0.99894130f,
 0.99879545f, 0.99864024f, 0.99847555f, 0.99830157f, 0.99811810f, 0.99792528f, 0.99772304f, 0.99751145f, 0.99729043f, 0.99706006f, 0.99682027f, 0.99657112f, 0.99631262f, 0.99604470f, 0.99576741f, 0.99548078f,
 0.99518472f, 0.99487931f, 0.99456459f, 0.99424046f, 0.99390697f, 0.99356413f, 0.99321193f, 0.99285042f, 0.99247950f, 0.99209929f, 0.99170977f, 0.99131083f, 0.99090260f, 0.99048507f, 0.99005818f, 0.98962200f,
 0.98917651f, 0.98872167f, 0.98825759f, 0.98778415f, 0.98730141f, 0.98680937f, 0.98630810f, 0.98579752f, 0.98527765f, 0.98474848f, 0.98421007f, 0.98366243f, 0.98310548f, 0.98253930f, 0.98196387f, 0.98137921f,
 0.98078525f, 0.98018211f, 0.97956973f, 0.97894818f, 0.97831738f, 0.97767735f, 0.97702813f, 0.97636974f, 0.97570211f, 0.97502536f, 0.97433937f, 0.97364426f, 0.97293997f, 0.97222650f, 0.97150385f, 0.97077215f,
 0.97003126f, 0.96928120f, 0.96852207f, 0.96775383f, 0.96697646f, 0.96618998f, 0.96539444f, 0.96458977f, 0.96377605f, 0.96295327f, 0.96212137f, 0.96128047f, 0.96043050f, 0.95957148f, 0.95870346f, 0.95782638f,
 0.95694029f, 0.95604521f, 0.95514113f, 0.95422810f, 0.95330602f, 0.95237499f, 0.95143503f, 0.95048606f, 0.94952816f, 0.94856131f, 0.94758558f, 0.94660091f, 0.94560730f, 0.94460481f, 0.94359344f, 0.94257319f,
 0.94154406f, 0.94050604f, 0.93945920f, 0.93840349f, 0.93733901f, 0.93626565f, 0.93518347f, 0.93409252f, 0.93299276f, 0.93188423f, 0.93076694f, 0.92964089f, 0.92850608f, 0.92736250f, 0.92621022f, 0.92504925f,
 0.92387950f, 0.92270112f, 0.92151403f, 0.92031825f, 0.91911381f, 0.91790074f, 0.91667902f, 0.91544867f, 0.91420972f, 0.91296214f, 0.91170603f, 0.91044128f, 0.90916795f, 0.90788609f, 0.90659571f, 0.90529674f,
 0.90398926f, 0.90267330f, 0.90134883f, 0.90001589f, 0.89867443f, 0.89732456f, 0.89596623f, 0.89459944f, 0.89322430f, 0.89184070f, 0.89044869f, 0.88904834f, 0.88763958f, 0.88622248f, 0.88479710f, 0.88336331f,
 0.88192123f, 0.88047087f, 0.87901223f, 0.87754524f, 0.87607008f, 0.87458664f, 0.87309498f, 0.87159508f, 0.87008697f, 0.86857069f, 0.86704624f, 0.86551362f, 0.86397284f, 0.86242390f, 0.86086690f, 0.85930181f,
 0.85772860f, 0.85614729f, 0.85455793f, 0.85296059f, 0.85135514f, 0.84974176f, 0.84812033f, 0.84649092f, 0.84485352f, 0.84320819f, 0.84155494f, 0.83989376f, 0.83822465f, 0.83654767f, 0.83486283f, 0.83317012f,
 0.83146960f, 0.82976121f, 0.82804501f, 0.82632101f, 0.82458925f, 0.82284975f, 0.82110250f, 0.81934750f, 0.81758475f, 0.81581438f, 0.81403631f, 0.81225055f, 0.81045717f, 0.80865616f, 0.80684751f, 0.80503130f,
 0.80320752f, 0.80137616f, 0.79953724f, 0.79769081f, 0.79583687f, 0.79397541f, 0.79210657f, 0.79023015f, 0.78834641f, 0.78645515f, 0.78455657f, 0.78265053f, 0.78073716f, 0.77881646f, 0.77688843f, 0.77495307f,
 0.77301043f, 0.77106047f, 0.76910329f, 0.76713890f, 0.76516724f, 0.76318836f, 0.76120234f, 0.75920916f, 0.75720882f, 0.75520134f, 0.75318676f, 0.75116509f, 0.74913633f, 0.74710059f, 0.74505776f, 0.74300790f,
 0.74095106f, 0.73888731f, 0.73681653f, 0.73473883f, 0.73265421f, 0.73056275f, 0.72846437f, 0.72635913f, 0.72424704f, 0.72212815f, 0.72000247f, 0.71787000f, 0.71573079f, 0.71358484f, 0.71143216f, 0.70927280f,
 0.70710671f, 0.70493406f, 0.70275468f, 0.70056874f, 0.69837618f, 0.69617707f, 0.69397140f, 0.69175923f, 0.68954051f, 0.68731529f, 0.68508363f, 0.68284547f, 0.68060094f, 0.67834997f, 0.67609262f, 0.67382896f,
 0.67155892f, 0.66928256f, 0.66699988f, 0.66471094f, 0.66241574f, 0.66011429f, 0.65780663f, 0.65549278f, 0.65317279f, 0.65084666f, 0.64851433f, 0.64617598f, 0.64383149f, 0.64148098f, 0.63912439f, 0.63676178f,
 0.63439322f, 0.63201869f, 0.62963820f, 0.62725174f, 0.62485945f, 0.62246120f, 0.62005717f, 0.61764723f, 0.61523151f, 0.61281002f, 0.61038274f, 0.60794973f, 0.60551101f, 0.60306656f, 0.60061640f, 0.59816062f,
 0.59569925f, 0.59323221f, 0.59075963f, 0.58828151f, 0.58579779f, 0.58330858f, 0.58081388f, 0.57831377f, 0.57580811f, 0.57329708f, 0.57078069f, 0.56825888f, 0.56573176f, 0.56319928f, 0.56066149f, 0.55811846f,
 0.55557019f, 0.55301666f, 0.55045789f, 0.54789400f, 0.54532492f, 0.54275072f, 0.54017138f, 0.53758699f, 0.53499758f, 0.53240305f, 0.52980357f, 0.52719909f, 0.52458960f, 0.52197522f, 0.51935595f, 0.51673174f,
 0.51410270f, 0.51146877f, 0.50883007f, 0.50618660f, 0.50353831f, 0.50088531f, 0.49822760f, 0.49556521f, 0.49289814f, 0.49022642f, 0.48755011f, 0.48486918f, 0.48218369f, 0.47949371f, 0.47679916f, 0.47410014f,
 0.47139668f, 0.46868876f, 0.46597642f, 0.46325973f, 0.46053866f, 0.45781323f, 0.45508352f, 0.45234951f, 0.44961128f, 0.44686878f, 0.44412208f, 0.44137120f, 0.43861616f, 0.43585700f, 0.43309376f, 0.43032640f,
 0.42755502f, 0.42477962f, 0.42200020f, 0.41921681f, 0.41642949f, 0.41363823f, 0.41084310f, 0.40804410f, 0.40524125f, 0.40243459f, 0.39962414f, 0.39680991f, 0.39399198f, 0.39117032f, 0.38834497f, 0.38551599f,
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 -0.63439316f, -0.63201863f, -0.62963814f, -0.62725168f, -0.62485939f, -0.62246114f, -0.62005711f, -0.61764717f, -0.61523145f, -0.61280996f, -0.61038268f, -0.60794967f, -0.60551089f, -0.60306644f, -0.60061634f, -0.59816056f,
 -0.59569919f, -0.59323215f, -0.59075958f, -0.58828139f, -0.58579773f, -0.58330852f, -0.58081383f, -0.57831365f, -0.57580805f, -0.57329702f, -0.57078063f, -0.56825882f, -0.56573170f, -0.56319922f, -0.56066144f, -0.55811840f,
 -0.55557013f, -0.55301660f, -0.55045784f, -0.54789394f, -0.54532486f, -0.54275066f, -0.54017133f, -0.53758693f, -0.53499746f, -0.53240299f, -0.52980351f, -0.52719897f, -0.52458954f, -0.52197516f, -0.51935583f, -0.51673168f,
 -0.51410258f, -0.51146871f, -0.50883001f, -0.50618649f, -0.50353825f, -0.50088525f, -0.49822754f, -0.49556512f, -0.49289805f, -0.49022636f, -0.48755002f, -0.48486909f, -0.48218364f, -0.47949362f, -0.47679910f, -0.47410008f,
 -0.47139660f, -0.46868867f, -0.46597636f, -0.46325964f, -0.46053857f, -0.45781317f, -0.45508343f, -0.45234945f, -0.44961119f, -0.44686869f, -0.44412199f, -0.44137111f, -0.43861610f, -0.43585694f, -0.43309367f, -0.43032634f,
 -0.42755494f, -0.42477953f, -0.42200011f, -0.41921675f, -0.41642940f, -0.41363817f, -0.41084301f, -0.40804401f, -0.40524116f, -0.40243450f, -0.39962405f, -0.39680985f, -0.39399189f, -0.39117023f, -0.38834488f, -0.38551590f,
 -0.38268328f, -0.37984705f, -0.37700725f, -0.37416390f, -0.37131703f, -0.36846668f, -0.36561283f, -0.36275557f, -0.35989487f, -0.35703081f, -0.35416338f, -0.35129261f, -0.34841853f, -0.34554118f, -0.34266058f, -0.33977672f,
 -0.33688968f, -0.33399948f, -0.33110616f, -0.32820970f, -0.32531014f, -0.32240751f, -0.31950188f, -0.31659323f, -0.31368157f, -0.31076699f, -0.30784950f, -0.30492908f, -0.30200580f, -0.29907966f, -0.29615074f, -0.29321900f,
 -0.29028451f, -0.28734729f, -0.28440738f, -0.28146479f, -0.27851954f, -0.27557164f, -0.27262118f, -0.26966816f, -0.26671261f, -0.26375452f, -0.26079395f, -0.25783095f, -0.25486550f, -0.25189766f, -0.24892744f, -0.24595489f,
 -0.24298002f, -0.24000286f, -0.23702344f, -0.23404180f, -0.23105794f, -0.22807191f, -0.22508375f, -0.22209346f, -0.21910107f, -0.21610664f, -0.21311015f, -0.21011168f, -0.20711121f, -0.20410880f, -0.20110446f, -0.19809824f,
 -0.19509016f, -0.19208023f, -0.18906850f, -0.18605499f, -0.18303972f, -0.18002273f, -0.17700405f, -0.17398371f, -0.17096172f, -0.16793813f, -0.16491295f, -0.16188623f, -0.15885797f, -0.15582822f, -0.15279701f, -0.14976436f,
 -0.14673030f, -0.14369486f, -0.14065807f, -0.13761996f, -0.13458054f, -0.13153987f, -0.12849794f, -0.12545481f, -0.12241051f, -0.11936504f, -0.11631846f, -0.11327078f, -0.11022203f, -0.10717225f, -0.10412146f, -0.10106969f,
 -0.09801697f, -0.09496333f, -0.09190878f, -0.08885338f, -0.08579714f, -0.08274009f, -0.07968227f, -0.07662369f, -0.07356439f, -0.07050440f, -0.06744374f, -0.06438246f, -0.06132056f, -0.05825809f, -0.05519507f, -0.05213153f,
 -0.04906750f, -0.04600301f, -0.04293808f, -0.03987275f, -0.03680705f, -0.03374100f, -0.03067463f, -0.02760797f, -0.02454105f, -0.02147391f, -0.01840656f, -0.01533903f, -0.01227136f, -0.00920358f, -0.00613571f, -0.00306778f
};


float gaia::s_TangentTable[TRIG_TABLE_SIZE]=
{
 0.00000000f, 0.00306797f, 0.00613600f, 0.00920414f, 0.01227246f, 0.01534101f, 0.01840985f, 0.02147903f, 0.02454862f, 0.02761867f, 0.03068925f, 0.03376039f, 0.03683218f, 0.03990466f, 0.04297790f, 0.04605194f,
 0.04912685f, 0.05220269f, 0.05527952f, 0.05835738f, 0.06143636f, 0.06451648f, 0.06759784f, 0.07068047f, 0.07376444f, 0.07684980f, 0.07993662f, 0.08302495f, 0.08611485f, 0.08920639f, 0.09229963f, 0.09539461f,
 0.09849141f, 0.10159007f, 0.10469068f, 0.10779327f, 0.11089791f, 0.11400467f, 0.11711361f, 0.12022477f, 0.12333824f, 0.12645406f, 0.12957230f, 0.13269302f, 0.13581628f, 0.13894215f, 0.14207068f, 0.14520194f,
 0.14833599f, 0.15147290f, 0.15461272f, 0.15775552f, 0.16090137f, 0.16405033f, 0.16720244f, 0.17035781f, 0.17351647f, 0.17667849f, 0.17984395f, 0.18301289f, 0.18618540f, 0.18936154f, 0.19254138f, 0.19572496f,
 0.19891237f, 0.20210367f, 0.20529895f, 0.20849824f, 0.21170163f, 0.21490918f, 0.21812098f, 0.22133705f, 0.22455752f, 0.22778241f, 0.23101182f, 0.23424581f, 0.23748446f, 0.24072783f, 0.24397598f, 0.24722901f,
 0.25048697f, 0.25374994f, 0.25701800f, 0.26029122f, 0.26356965f, 0.26685342f, 0.27014256f, 0.27343714f, 0.27673727f, 0.28004301f, 0.28335443f, 0.28667161f, 0.28999463f, 0.29332358f, 0.29665852f, 0.29999954f,
 0.30334669f, 0.30670011f, 0.31005982f, 0.31342593f, 0.31679854f, 0.32017770f, 0.32356352f, 0.32695603f, 0.33035538f, 0.33376163f, 0.33717486f, 0.34059516f, 0.34402260f, 0.34745732f, 0.35089934f, 0.35434878f,
 0.35780573f, 0.36127028f, 0.36474252f, 0.36822253f, 0.37171042f, 0.37520629f, 0.37871021f, 0.38222227f, 0.38574257f, 0.38927123f, 0.39280832f, 0.39635396f, 0.39990821f, 0.40347120f, 0.40704304f, 0.41062379f,
 0.41421357f, 0.41781250f, 0.42142066f, 0.42503816f, 0.42866513f, 0.43230164f, 0.43594781f, 0.43960372f, 0.44326952f, 0.44694531f, 0.45063120f, 0.45432729f, 0.45803371f, 0.46175054f, 0.46547791f, 0.46921596f,
 0.47296479f, 0.47672451f, 0.48049524f, 0.48427710f, 0.48807022f, 0.49187472f, 0.49569073f, 0.49951833f, 0.50335771f, 0.50720894f, 0.51107222f, 0.51494759f, 0.51883525f, 0.52273530f, 0.52664787f, 0.53057313f,
 0.53451115f, 0.53846210f, 0.54242617f, 0.54640347f, 0.55039406f, 0.55439818f, 0.55841595f, 0.56244755f, 0.56649303f, 0.57055259f, 0.57462645f, 0.57871461f, 0.58281738f, 0.58693486f, 0.59106714f, 0.59521449f,
 0.59937698f, 0.60355479f, 0.60774809f, 0.61195713f, 0.61618197f, 0.62042278f, 0.62467980f, 0.62895316f, 0.63324302f, 0.63754964f, 0.64187306f, 0.64621359f, 0.65057141f, 0.65494657f, 0.65933943f, 0.66375005f,
 0.66817868f, 0.67262548f, 0.67709070f, 0.68157452f, 0.68607712f, 0.69059867f, 0.69513947f, 0.69969964f, 0.70427948f, 0.70887911f, 0.71349883f, 0.71813881f, 0.72279930f, 0.72748047f, 0.73218256f, 0.73690587f,
 0.74165058f, 0.74641693f, 0.75120515f, 0.75601548f, 0.76084816f, 0.76570350f, 0.77058172f, 0.77548301f, 0.78040767f, 0.78535599f, 0.79032826f, 0.79532462f, 0.80034548f, 0.80539101f, 0.81046158f, 0.81555742f,
 0.82067883f, 0.82582605f, 0.83099949f, 0.83619934f, 0.84142590f, 0.84667957f, 0.85196060f, 0.85726929f, 0.86260599f, 0.86797100f, 0.87336463f, 0.87878728f, 0.88423926f, 0.88972086f, 0.89523250f, 0.90077448f,
 0.90634722f, 0.91195101f, 0.91758621f, 0.92325330f, 0.92895252f, 0.93468434f, 0.94044912f, 0.94624728f, 0.95207918f, 0.95794529f, 0.96384591f, 0.96978158f, 0.97575271f, 0.98175967f, 0.98780286f, 0.99388289f,
 1.00000000f, 1.00615489f, 1.01234782f, 1.01857936f, 1.02484989f, 1.03116012f, 1.03751028f, 1.04390109f, 1.05033290f, 1.05680633f, 1.06332183f, 1.06988001f, 1.07648134f, 1.08312654f, 1.08981597f, 1.09655023f,
 1.10333002f, 1.11015582f, 1.11702836f, 1.12394810f, 1.13091576f, 1.13793194f, 1.14499724f, 1.15211236f, 1.15927792f, 1.16649473f, 1.17376328f, 1.18108451f, 1.18845892f, 1.19588721f, 1.20337033f, 1.21090889f,
 1.21850359f, 1.22615528f, 1.23386490f, 1.24163294f, 1.24946058f, 1.25734830f, 1.26529717f, 1.27330804f, 1.28138161f, 1.28951907f, 1.29772103f, 1.30598867f, 1.31432271f, 1.32272434f, 1.33119440f, 1.33973396f,
 1.34834397f, 1.35702550f, 1.36577964f, 1.37460744f, 1.38351011f, 1.39248860f, 1.40154409f, 1.41067779f, 1.41989100f, 1.42918479f, 1.43856037f, 1.44801915f, 1.45756233f, 1.46719122f, 1.47690713f, 1.48671162f,
 1.49660587f, 1.50659144f, 1.51666975f, 1.52684224f, 1.53711045f, 1.54747605f, 1.55794048f, 1.56850553f, 1.57917261f, 1.58994365f, 1.60082030f, 1.61180425f, 1.62289739f, 1.63410163f, 1.64541864f, 1.65685058f,
 1.66839933f, 1.68006682f, 1.69185531f, 1.70376682f, 1.71580350f, 1.72796750f, 1.74026120f, 1.75268698f, 1.76524699f, 1.77794385f, 1.79077995f, 1.80375791f, 1.81688023f, 1.83014965f, 1.84356904f, 1.85714102f,
 1.87086856f, 1.88475454f, 1.89880216f, 1.91301429f, 1.92739427f, 1.94194531f, 1.95667088f, 1.97157419f, 1.98665893f, 2.00192881f, 2.01738715f, 2.03303814f, 2.04888558f, 2.06493378f, 2.08118629f, 2.09764791f,
 2.11432242f, 2.13121510f, 2.14832973f, 2.16567183f, 2.18324566f, 2.20105672f, 2.21910977f, 2.23741055f, 2.25596404f, 2.27477622f, 2.29385304f, 2.31320000f, 2.33282351f, 2.35273027f, 2.37292624f, 2.39341831f,
 2.41421390f, 2.43531942f, 2.45674300f, 2.47849202f, 2.50057411f, 2.52299786f, 2.54577112f, 2.56890321f, 2.59240270f, 2.61627913f, 2.64054179f, 2.66520095f, 2.69026661f, 2.71574926f, 2.74166036f, 2.76801109f,
 2.79481316f, 2.82207870f, 2.84982061f, 2.87805176f, 2.90678620f, 2.93603754f, 2.96582055f, 2.99615073f, 3.02704358f, 3.05851555f, 3.09058380f, 3.12326622f, 3.15658069f, 3.19054699f, 3.22518468f, 3.26051474f,
 3.29655862f, 3.33333921f, 3.37087965f, 3.40920496f, 3.44834018f, 3.48831248f, 3.52914953f, 3.57088065f, 3.61353612f, 3.65714812f, 3.70174980f, 3.74737620f, 3.79406404f, 3.84185147f, 3.89077878f, 3.94088840f,
 3.99222445f, 4.04483366f, 4.09876490f, 4.15406990f, 4.21080256f, 4.26902056f, 4.32878351f, 4.39015532f, 4.45320320f, 4.51799726f, 4.58461285f, 4.65312910f, 4.72363043f, 4.79620457f, 4.87094688f, 4.94795656f,
 5.02734041f, 5.10921144f, 5.19369030f, 5.28090477f, 5.37099171f, 5.46409702f, 5.56037760f, 5.65999985f, 5.76314354f, 5.86999989f, 5.98077536f, 6.09569216f, 6.21498919f, 6.33892393f, 6.46777487f, 6.60184288f,
 6.74145412f, 6.88696241f, 7.03875208f, 7.19724226f, 7.36288977f, 7.53619385f, 7.71770144f, 7.90801287f, 8.10778809f, 8.31775665f, 8.53872108f, 8.77157402f, 9.01730537f, 9.27702045f, 9.55195332f, 9.84348583f,
 10.15317440f, 10.48277760f, 10.83428574f, 11.20996475f, 11.61240482f, 12.04457855f, 12.50991821f, 13.01240349f, 13.55667686f, 14.14818954f, 14.79338264f, 15.49992466f, 16.27701950f, 17.13580513f, 18.08989716f, 19.15611649f,
 20.35548592f, 21.71463203f, 23.26779938f, 25.05975533f, 27.15020180f, 29.62054443f, 32.58475113f, 36.20744324f, 40.73555374f, 46.55712509f, 54.31887817f, 65.18493652f, 81.48352814f, 108.64721680f, 162.97377014f, 325.95294189f,
 -22877332.00000000f, -325.94363403f, -162.97145081f, -108.64618683f, -81.48294830f, -65.18456268f, -54.31861877f, -46.55693436f, -40.73540878f, -36.20732880f, -32.58465958f, -29.62046814f, -27.15013695f, -25.05970001f, -23.26775169f, -21.71459198f,
 -20.35544968f, -19.15608406f, -18.08986855f, -17.13577843f, -16.27699661f, -15.49990368f, -14.79336357f, -14.14817142f, -13.55666065f, -13.01238918f, -12.50990486f, -12.04456615f, -11.61239243f, -11.20995331f, -10.83427525f, -10.48276806f,
 -10.15316582f, -9.84347725f, -9.55194473f, -9.27701378f, -9.01729870f, -8.77156639f, -8.53871441f, -8.31774998f, -8.10778236f, -7.90800762f, -7.71769619f, -7.53618908f, -7.36288500f, -7.19723797f, -7.03874779f, -6.88695812f,
 -6.74145031f, -6.60183907f, -6.46777153f, -6.33892059f, -6.21498585f, -6.09568882f, -5.98077202f, -5.86999655f, -5.76314020f, -5.65999699f, -5.56037474f, -5.46409464f, -5.37098885f, -5.28090191f, -5.19368792f, -5.10920906f,
 -5.02733803f, -4.94795418f, -4.87094450f, -4.79620266f, -4.72362804f, -4.65312719f, -4.58461094f, -4.51799536f, -4.45320129f, -4.39015388f, -4.32878208f, -4.26901865f, -4.21080112f, -4.15406847f, -4.09876347f, -4.04483223f,
 -3.99222302f, -3.94088697f, -3.89077735f, -3.84185004f, -3.79406261f, -3.74737501f, -3.70174861f, -3.65714693f, -3.61353493f, -3.57087946f, -3.52914834f, -3.48831129f, -3.44833899f, -3.40920377f, -3.37087870f, -3.33333802f,
 -3.29655766f, -3.26051354f, -3.22518373f, -3.19054604f, -3.15657973f, -3.12326527f, -3.09058285f, -3.05851460f, -3.02704263f, -2.99614978f, -2.96581984f, -2.93603659f, -2.90678525f, -2.87805104f, -2.84981966f, -2.82207799f,
 -2.79481220f, -2.76801038f, -2.74165964f, -2.71574855f, -2.69026589f, -2.66520023f, -2.64054108f, -2.61627841f, -2.59240222f, -2.56890249f, -2.54577065f, -2.52299714f, -2.50057340f, -2.47849131f, -2.45674253f, -2.43531895f,
 -2.41421318f, -2.39341784f, -2.37292552f, -2.35272956f, -2.33282304f, -2.31319952f, -2.29385233f, -2.27477574f, -2.25596356f, -2.23740983f, -2.21910930f, -2.20105624f, -2.18324518f, -2.16567135f, -2.14832926f, -2.13121462f,
 -2.11432195f, -2.09764743f, -2.08118582f, -2.06493330f, -2.04888535f, -2.03303766f, -2.01738667f, -2.00192833f, -1.98665845f, -1.97157383f, -1.95667040f, -1.94194496f, -1.92739391f, -1.91301394f, -1.89880168f, -1.88475418f,
 -1.87086821f, -1.85714066f, -1.84356868f, -1.83014929f, -1.81687987f, -1.80375743f, -1.79077959f, -1.77794349f, -1.76524663f, -1.75268662f, -1.74026096f, -1.72796714f, -1.71580315f, -1.70376647f, -1.69185495f, -1.68006659f,
 -1.66839898f, -1.65685022f, -1.64541841f, -1.63410127f, -1.62289715f, -1.61180401f, -1.60081995f, -1.58994341f, -1.57917237f, -1.56850517f, -1.55794024f, -1.54747581f, -1.53711021f, -1.52684188f, -1.51666939f, -1.50659108f,
 -1.49660552f, -1.48671126f, -1.47690690f, -1.46719086f, -1.45756197f, -1.44801891f, -1.43856013f, -1.42918444f, -1.41989076f, -1.41067755f, -1.40154386f, -1.39248836f, -1.38350987f, -1.37460721f, -1.36577940f, -1.35702527f,
 -1.34834373f, -1.33973372f, -1.33119416f, -1.32272410f, -1.31432247f, -1.30598843f, -1.29772079f, -1.28951883f, -1.28138137f, -1.27330780f, -1.26529694f, -1.25734806f, -1.24946034f, -1.24163282f, -1.23386467f, -1.22615516f,
 -1.21850336f, -1.21090865f, -1.20337009f, -1.19588697f, -1.18845868f, -1.18108428f, -1.17376316f, -1.16649449f, -1.15927780f, -1.15211213f, -1.14499700f, -1.13793170f, -1.13091552f, -1.12394786f, -1.11702812f, -1.11015570f,
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 0.00000009f, 0.00306806f, 0.00613609f, 0.00920423f, 0.01227255f, 0.01534110f, 0.01840994f, 0.02147912f, 0.02454871f, 0.02761876f, 0.03068933f, 0.03376048f, 0.03683227f, 0.03990475f, 0.04297798f, 0.04605203f,
 0.04912694f, 0.05220278f, 0.05527960f, 0.05835747f, 0.06143644f, 0.06451657f, 0.06759793f, 0.07068055f, 0.07376452f, 0.07684989f, 0.07993671f, 0.08302504f, 0.08611494f, 0.08920648f, 0.09229971f, 0.09539470f,
 0.09849150f, 0.10159016f, 0.10469076f, 0.10779335f, 0.11089800f, 0.11400476f, 0.11711369f, 0.12022486f, 0.12333833f, 0.12645414f, 0.12957239f, 0.13269311f, 0.13581637f, 0.13894224f, 0.14207077f, 0.14520203f,
 0.14833608f, 0.15147299f, 0.15461281f, 0.15775561f, 0.16090146f, 0.16405042f, 0.16720253f, 0.17035790f, 0.17351656f, 0.17667858f, 0.17984404f, 0.18301299f, 0.18618549f, 0.18936163f, 0.19254147f, 0.19572505f,
 0.19891246f, 0.20210376f, 0.20529903f, 0.20849833f, 0.21170172f, 0.21490927f, 0.21812107f, 0.22133715f, 0.22455761f, 0.22778250f, 0.23101191f, 0.23424591f, 0.23748454f, 0.24072792f, 0.24397607f, 0.24722910f,
 0.25048706f, 0.25375003f, 0.25701809f, 0.26029131f, 0.26356977f, 0.26685351f, 0.27014264f, 0.27343726f, 0.27673736f, 0.28004310f, 0.28335452f, 0.28667170f, 0.28999472f, 0.29332367f, 0.29665861f, 0.29999962f,
 0.30334678f, 0.30670020f, 0.31005991f, 0.31342605f, 0.31679863f, 0.32017779f, 0.32356361f, 0.32695612f, 0.33035550f, 0.33376172f, 0.33717495f, 0.34059525f, 0.34402272f, 0.34745741f, 0.35089943f, 0.35434887f,
 0.35780582f, 0.36127037f, 0.36474264f, 0.36822265f, 0.37171054f, 0.37520638f, 0.37871030f, 0.38222235f, 0.38574266f, 0.38927132f, 0.39280844f, 0.39635405f, 0.39990830f, 0.40347129f, 0.40704313f, 0.41062388f,
 0.41421369f, 0.41781262f, 0.42142075f, 0.42503828f, 0.42866522f, 0.43230173f, 0.43594790f, 0.43960384f, 0.44326964f, 0.44694543f, 0.45063132f, 0.45432740f, 0.45803380f, 0.46175066f, 0.46547803f, 0.46921608f,
 0.47296491f, 0.47672462f, 0.48049536f, 0.48427722f, 0.48807034f, 0.49187484f, 0.49569082f, 0.49951845f, 0.50335783f, 0.50720906f, 0.51107234f, 0.51494771f, 0.51883537f, 0.52273542f, 0.52664798f, 0.53057325f,
 0.53451127f, 0.53846222f, 0.54242629f, 0.54640359f, 0.55039418f, 0.55439830f, 0.55841607f, 0.56244767f, 0.56649315f, 0.57055271f, 0.57462656f, 0.57871473f, 0.58281749f, 0.58693492f, 0.59106725f, 0.59521461f,
 0.59937710f, 0.60355490f, 0.60774821f, 0.61195725f, 0.61618209f, 0.62042290f, 0.62467992f, 0.62895328f, 0.63324314f, 0.63754976f, 0.64187324f, 0.64621371f, 0.65057153f, 0.65494668f, 0.65933955f, 0.66375017f,
 0.66817880f, 0.67262560f, 0.67709082f, 0.68157464f, 0.68607724f, 0.69059879f, 0.69513959f, 0.69969982f, 0.70427960f, 0.70887929f, 0.71349895f, 0.71813893f, 0.72279942f, 0.72748059f, 0.73218274f, 0.73690599f,
 0.74165070f, 0.74641705f, 0.75120527f, 0.75601560f, 0.76084834f, 0.76570362f, 0.77058184f, 0.77548313f, 0.78040785f, 0.78535616f, 0.79032838f, 0.79532480f, 0.80034560f, 0.80539119f, 0.81046176f, 0.81555760f,
 0.82067895f, 0.82582623f, 0.83099961f, 0.83619946f, 0.84142607f, 0.84667969f, 0.85196072f, 0.85726941f, 0.86260611f, 0.86797112f, 0.87336481f, 0.87878746f, 0.88423944f, 0.88972104f, 0.89523268f, 0.90077466f,
 0.90634739f, 0.91195112f, 0.91758639f, 0.92325342f, 0.92895269f, 0.93468451f, 0.94044930f, 0.94624746f, 0.95207936f, 0.95794547f, 0.96384609f, 0.96978176f, 0.97575289f, 0.98175979f, 0.98780304f, 0.99388301f,
 1.00000024f, 1.00615501f, 1.01234794f, 1.01857948f, 1.02485013f, 1.03116024f, 1.03751051f, 1.04390121f, 1.05033302f, 1.05680645f, 1.06332207f, 1.06988025f, 1.07648158f, 1.08312666f, 1.08981609f, 1.09655046f,
 1.10333025f, 1.11015606f, 1.11702859f, 1.12394834f, 1.13091600f, 1.13793206f, 1.14499748f, 1.15211260f, 1.15927815f, 1.16649497f, 1.17376351f, 1.18108463f, 1.18845904f, 1.19588745f, 1.20337057f, 1.21090901f,
 1.21850383f, 1.22615552f, 1.23386514f, 1.24163318f, 1.24946070f, 1.25734854f, 1.26529741f, 1.27330828f, 1.28138185f, 1.28951931f, 1.29772127f, 1.30598891f, 1.31432295f, 1.32272458f, 1.33119464f, 1.33973420f,
 1.34834421f, 1.35702574f, 1.36577988f, 1.37460780f, 1.38351035f, 1.39248884f, 1.40154433f, 1.41067815f, 1.41989124f, 1.42918503f, 1.43856061f, 1.44801939f, 1.45756257f, 1.46719146f, 1.47690749f, 1.48671186f,
 1.49660611f, 1.50659168f, 1.51666999f, 1.52684247f, 1.53711081f, 1.54747641f, 1.55794084f, 1.56850576f, 1.57917297f, 1.58994401f, 1.60082066f, 1.61180460f, 1.62289774f, 1.63410187f, 1.64541900f, 1.65685093f,
 1.66839969f, 1.68006718f, 1.69185567f, 1.70376718f, 1.71580386f, 1.72796786f, 1.74026155f, 1.75268734f, 1.76524734f, 1.77794421f, 1.79078031f, 1.80375826f, 1.81688058f, 1.83015013f, 1.84356940f, 1.85714138f,
 1.87086892f, 1.88475502f, 1.89880252f, 1.91301477f, 1.92739475f, 1.94194579f, 1.95667124f, 1.97157466f, 1.98665941f, 2.00192904f, 2.01738763f, 2.03303862f, 2.04888606f, 2.06493425f, 2.08118677f, 2.09764814f,
 2.11432290f, 2.13121557f, 2.14833045f, 2.16567230f, 2.18324614f, 2.20105720f, 2.21911025f, 2.23741102f, 2.25596452f, 2.27477670f, 2.29385352f, 2.31320047f, 2.33282423f, 2.35273075f, 2.37292671f, 2.39341903f,
 2.41421437f, 2.43532014f, 2.45674372f, 2.47849250f, 2.50057483f, 2.52299833f, 2.54577184f, 2.56890392f, 2.59240341f, 2.61627984f, 2.64054251f, 2.66520166f, 2.69026732f, 2.71574998f, 2.74166107f, 2.76801181f,
 2.79481387f, 2.82207942f, 2.84982133f, 2.87805271f, 2.90678692f, 2.93603826f, 2.96582150f, 2.99615145f, 3.02704453f, 3.05851650f, 3.09058475f, 3.12326694f, 3.15658164f, 3.19054794f, 3.22518563f, 3.26051569f,
 3.29655957f, 3.33334017f, 3.37088084f, 3.40920591f, 3.44834137f, 3.48831367f, 3.52915072f, 3.57088184f, 3.61353731f, 3.65714931f, 3.70175123f, 3.74737763f, 3.79406524f, 3.84185266f, 3.89078021f, 3.94088984f,
 3.99222589f, 4.04483509f, 4.09876633f, 4.15407133f, 4.21080446f, 4.26902246f, 4.32878542f, 4.39015722f, 4.45320463f, 4.51799917f, 4.58461475f, 4.65313148f, 4.72363234f, 4.79620647f, 4.87094879f, 4.94795895f,
 5.02734280f, 5.10921383f, 5.19369268f, 5.28090715f, 5.37099409f, 5.46409988f, 5.56038046f, 5.66000271f, 5.76314640f, 5.87000275f, 5.98077869f, 6.09569550f, 6.21499300f, 6.33892775f, 6.46777868f, 6.60184717f,
 6.74145842f, 6.88696671f, 7.03875685f, 7.19724703f, 7.36289454f, 7.53619909f, 7.71770668f, 7.90801859f, 8.10779476f, 8.31776237f, 8.53872681f, 8.77158070f, 9.01731300f, 9.27702808f, 9.55196095f, 9.84349442f,
 10.15318394f, 10.48278713f, 10.83429527f, 11.20997524f, 11.61241627f, 12.04459190f, 12.50993252f, 13.01241875f, 13.55669308f, 14.14820671f, 14.79340172f, 15.49994564f, 16.27704239f, 17.13583183f, 18.08992767f, 19.15614891f,
 20.35552216f, 21.71467400f, 23.26784515f, 25.05981064f, 27.15026665f, 29.62062073f, 32.58484268f, 36.20755768f, 40.73569870f, 46.55731201f, 54.31913757f, 65.18531036f, 81.48410797f, 108.64825439f, 162.97608948f, 325.96221924f,
 -7625777.50000000f, -325.93435669f, -162.96913147f, -108.64515686f, -81.48236847f, -65.18418884f, -54.31836319f, -46.55674362f, -40.73526382f, -36.20721436f, -32.58456421f, -29.62038994f, -27.15007401f, -25.05964661f, -23.26770401f, -21.71455002f,
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 -1.87086773f, -1.85714018f, -1.84356821f, -1.83014894f, -1.81687951f, -1.80375707f, -1.79077923f, -1.77794313f, -1.76524627f, -1.75268626f, -1.74026060f, -1.72796679f, -1.71580279f, -1.70376611f, -1.69185472f, -1.68006623f,
 -1.66839862f, -1.65684998f, -1.64541805f, -1.63410091f, -1.62289679f, -1.61180365f, -1.60081971f, -1.58994305f, -1.57917202f, -1.56850493f, -1.55793989f, -1.54747546f, -1.53710985f, -1.52684164f, -1.51666915f, -1.50659084f,
 -1.49660528f, -1.48671103f, -1.47690666f, -1.46719062f, -1.45756173f, -1.44801855f, -1.43855989f, -1.42918420f, -1.41989040f, -1.41067731f, -1.40154362f, -1.39248800f, -1.38350952f, -1.37460697f, -1.36577916f, -1.35702503f,
 -1.34834349f, -1.33973348f, -1.33119392f, -1.32272387f, -1.31432223f, -1.30598819f, -1.29772055f, -1.28951859f, -1.28138113f, -1.27330756f, -1.26529670f, -1.25734782f, -1.24946010f, -1.24163258f, -1.23386443f, -1.22615492f,
 -1.21850312f, -1.21090841f, -1.20336986f, -1.19588685f, -1.18845844f, -1.18108404f, -1.17376292f, -1.16649437f, -1.15927756f, -1.15211189f, -1.14499676f, -1.13793147f, -1.13091528f, -1.12394774f, -1.11702800f, -1.11015546f,
 -1.10332966f, -1.09654987f, -1.08981550f, -1.08312607f, -1.07648098f, -1.06987965f, -1.06332147f, -1.05680597f, -1.05033255f, -1.04390073f, -1.03750992f, -1.03115976f, -1.02484953f, -1.01857901f, -1.01234746f, -1.00615454f,
 -0.99999970f, -0.99388254f, -0.98780257f, -0.98175931f, -0.97575235f, -0.96978128f, -0.96384561f, -0.95794493f, -0.95207888f, -0.94624692f, -0.94044882f, -0.93468398f, -0.92895216f, -0.92325294f, -0.91758591f, -0.91195065f,
 -0.90634692f, -0.90077418f, -0.89523220f, -0.88972056f, -0.88423896f, -0.87878698f, -0.87336433f, -0.86797065f, -0.86260569f, -0.85726899f, -0.85196030f, -0.84667927f, -0.84142560f, -0.83619905f, -0.83099920f, -0.82582581f,
 -0.82067853f, -0.81555712f, -0.81046128f, -0.80539078f, -0.80034518f, -0.79532433f, -0.79032797f, -0.78535575f, -0.78040743f, -0.77548271f, -0.77058142f, -0.76570320f, -0.76084793f, -0.75601518f, -0.75120485f, -0.74641663f,
 -0.74165028f, -0.73690563f, -0.73218232f, -0.72748017f, -0.72279900f, -0.71813858f, -0.71349859f, -0.70887887f, -0.70427924f, -0.69969940f, -0.69513923f, -0.69059843f, -0.68607682f, -0.68157423f, -0.67709047f, -0.67262524f,
 -0.66817838f, -0.66374975f, -0.65933913f, -0.65494633f, -0.65057111f, -0.64621335f, -0.64187282f, -0.63754940f, -0.63324279f, -0.62895292f, -0.62467957f, -0.62042254f, -0.61618173f, -0.61195689f, -0.60774785f, -0.60355455f,
 -0.59937674f, -0.59521425f, -0.59106690f, -0.58693463f, -0.58281714f, -0.57871437f, -0.57462621f, -0.57055235f, -0.56649280f, -0.56244731f, -0.55841571f, -0.55439794f, -0.55039382f, -0.54640323f, -0.54242593f, -0.53846192f,
 -0.53451091f, -0.53057289f, -0.52664763f, -0.52273506f, -0.51883501f, -0.51494735f, -0.51107198f, -0.50720876f, -0.50335747f, -0.49951813f, -0.49569049f, -0.49187452f, -0.48807001f, -0.48427689f, -0.48049504f, -0.47672430f,
 -0.47296458f, -0.46921575f, -0.46547771f, -0.46175033f, -0.45803347f, -0.45432708f, -0.45063099f, -0.44694510f, -0.44326931f, -0.43960351f, -0.43594760f, -0.43230143f, -0.42866492f, -0.42503795f, -0.42142045f, -0.41781229f,
 -0.41421336f, -0.41062358f, -0.40704283f, -0.40347099f, -0.39990801f, -0.39635375f, -0.39280811f, -0.38927102f, -0.38574237f, -0.38222206f, -0.37871000f, -0.37520608f, -0.37171024f, -0.36822236f, -0.36474234f, -0.36127010f,
 -0.35780552f, -0.35434857f, -0.35089913f, -0.34745711f, -0.34402242f, -0.34059498f, -0.33717465f, -0.33376142f, -0.33035520f, -0.32695585f, -0.32356331f, -0.32017750f, -0.31679833f, -0.31342575f, -0.31005964f, -0.30669990f,
 -0.30334651f, -0.29999933f, -0.29665831f, -0.29332340f, -0.28999445f, -0.28667143f, -0.28335425f, -0.28004283f, -0.27673709f, -0.27343696f, -0.27014238f, -0.26685324f, -0.26356947f, -0.26029104f, -0.25701782f, -0.25374976f,
 -0.25048679f, -0.24722882f, -0.24397579f, -0.24072763f, -0.23748428f, -0.23424563f, -0.23101164f, -0.22778223f, -0.22455733f, -0.22133687f, -0.21812078f, -0.21490900f, -0.21170145f, -0.20849806f, -0.20529877f, -0.20210350f,
 -0.19891219f, -0.19572477f, -0.19254120f, -0.18936136f, -0.18618523f, -0.18301271f, -0.17984377f, -0.17667831f, -0.17351629f, -0.17035763f, -0.16720226f, -0.16405015f, -0.16090119f, -0.15775535f, -0.15461254f, -0.15147272f,
 -0.14833581f, -0.14520176f, -0.14207050f, -0.13894197f, -0.13581610f, -0.13269284f, -0.12957212f, -0.12645388f, -0.12333806f, -0.12022460f, -0.11711343f, -0.11400450f, -0.11089773f, -0.10779309f, -0.10469050f, -0.10158990f,
 -0.09849123f, -0.09539443f, -0.09229945f, -0.08920622f, -0.08611467f, -0.08302477f, -0.07993644f, -0.07684962f, -0.07376426f, -0.07068029f, -0.06759766f, -0.06451631f, -0.06143618f, -0.05835721f, -0.05527934f, -0.05220252f,
 -0.04912668f, -0.04605176f, -0.04297772f, -0.03990449f, -0.03683201f, -0.03376022f, -0.03068907f, -0.02761850f, -0.02454845f, -0.02147886f, -0.01840967f, -0.01534084f, -0.01227229f, -0.00920397f, -0.00613583f, -0.00306780f
};


uint32 gaia::fast_sqrt_table[0x10000]=
{
	3474675, 3474856, 3475037, 3475218, 3475399, 3475580, 3475761, 3475942, 3476123, 3476304, 3476485, 3476666, 3476847, 3477028, 3477209, 3477390, 3477571, 3477752, 3477933, 3478114, 3478295, 3478476, 3478657, 3478838, 3479019, 3479200, 3479381, 3479562, 3479743, 3479924, 3480105, 3480285, 3480466, 3480647, 3480828, 3481009, 3481190, 3481371, 3481552, 3481733, 3481914, 3482095, 3482276, 3482456, 3482637, 3482818, 3482999, 3483180, 3483361, 3483542, 3483723, 3483904, 3484084, 3484265, 3484446, 3484627, 3484808, 3484989, 3485170, 3485351, 3485531, 3485712, 3485893, 3486074, 3486255, 3486436, 3486616, 3486797, 3486978, 3487159, 3487340, 3487521, 3487701, 3487882, 3488063, 3488244, 3488425, 3488606, 3488786, 3488967, 3489148, 3489329, 3489510, 3489690, 3489871, 3490052, 3490233, 3490413, 3490594, 3490775, 3490956, 3491137, 3491317, 3491498, 3491679, 3491860, 3492040, 3492221, 3492402, 3492583, 3492763, 3492944, 3493125, 3493306, 3493486, 3493667, 3493848, 3494028, 3494209, 3494390, 3494571, 3494751, 3494932, 3495113, 3495293, 3495474, 3495655, 3495836, 3496016, 3496197, 3496378, 3496558, 3496739, 3496920, 3497100, 3497281, 3497462, 3497642, 
	3497823, 3498004, 3498184, 3498365, 3498546, 3498726, 3498907, 3499088, 3499268, 3499449, 3499630, 3499810, 3499991, 3500172, 3500352, 3500533, 3500713, 3500894, 3501075, 3501255, 3501436, 3501616, 3501797, 3501978, 3502158, 3502339, 3502520, 3502700, 3502881, 3503061, 3503242, 3503422, 3503603, 3503784, 3503964, 3504145, 3504325, 3504506, 3504686, 3504867, 3505048, 3505228, 3505409, 3505589, 3505770, 3505950, 3506131, 3506311, 3506492, 3506672, 3506853, 3507034, 3507214, 3507395, 3507575, 3507756, 3507936, 3508117, 3508297, 3508478, 3508658, 3508839, 3509019, 3509200, 3509380, 3509561, 3509741, 3509922, 3510102, 3510283, 3510463, 3510644, 3510824, 3511004, 3511185, 3511365, 3511546, 3511726, 3511907, 3512087, 3512268, 3512448, 3512629, 3512809, 3512989, 3513170, 3513350, 3513531, 3513711, 3513892, 3514072, 3514252, 3514433, 3514613, 3514794, 3514974, 3515154, 3515335, 3515515, 3515696, 3515876, 3516056, 3516237, 3516417, 3516598, 3516778, 3516958, 3517139, 3517319, 3517499, 3517680, 3517860, 3518041, 3518221, 3518401, 3518582, 3518762, 3518942, 3519123, 3519303, 3519483, 3519664, 3519844, 3520024, 3520205, 3520385, 3520565, 3520746, 
	3520926, 3521106, 3521287, 3521467, 3521647, 3521828, 3522008, 3522188, 3522368, 3522549, 3522729, 3522909, 3523090, 3523270, 3523450, 3523630, 3523811, 3523991, 3524171, 3524352, 3524532, 3524712, 3524892, 3525073, 3525253, 3525433, 3525613, 3525794, 3525974, 3526154, 3526334, 3526514, 3526695, 3526875, 3527055, 3527235, 3527416, 3527596, 3527776, 3527956, 3528136, 3528317, 3528497, 3528677, 3528857, 3529037, 3529218, 3529398, 3529578, 3529758, 3529938, 3530119, 3530299, 3530479, 3530659, 3530839, 3531019, 3531200, 3531380, 3531560, 3531740, 3531920, 3532100, 3532281, 3532461, 3532641, 3532821, 3533001, 3533181, 3533361, 3533541, 3533722, 3533902, 3534082, 3534262, 3534442, 3534622, 3534802, 3534982, 3535162, 3535343, 3535523, 3535703, 3535883, 3536063, 3536243, 3536423, 3536603, 3536783, 3536963, 3537143, 3537323, 3537504, 3537684, 3537864, 3538044, 3538224, 3538404, 3538584, 3538764, 3538944, 3539124, 3539304, 3539484, 3539664, 3539844, 3540024, 3540204, 3540384, 3540564, 3540744, 3540924, 3541104, 3541284, 3541464, 3541644, 3541824, 3542004, 3542184, 3542364, 3542544, 3542724, 3542904, 3543084, 3543264, 3543444, 3543624, 3543804, 
	3543984, 3544164, 3892880, 3893055, 3893230, 3893405, 3893580, 3893755, 3893929, 3894104, 3894279, 3894454, 3894629, 3894804, 3894978, 3895153, 3895328, 3895503, 3895678, 3895853, 3896027, 3896202, 3896377, 3896552, 3896727, 3896901, 3897076, 3897251, 3897426, 3897601, 3897775, 3897950, 3898125, 3898300, 3898474, 3898649, 3898824, 3898999, 3899174, 3899348, 3899523, 3899698, 3899873, 3900047, 3900222, 3900397, 3900572, 3900746, 3900921, 3901096, 3901271, 3901445, 3901620, 3901795, 3901969, 3902144, 3902319, 3902494, 3902668, 3902843, 3903018, 3903193, 3903367, 3903542, 3903717, 3903891, 3904066, 3904241, 3904415, 3904590, 3904765, 3904939, 3905114, 3905289, 3905464, 3905638, 3905813, 3905988, 3906162, 3906337, 3906512, 3906686, 3906861, 
	3907035, 3907210, 3907385, 3907559, 3907734, 3907909, 3908083, 3908258, 3908433, 3908607, 3908782, 3908957, 3909131, 3909306, 3909480, 3909655, 3909830, 3910004, 3910179, 3910353, 3910528, 3910703, 3910877, 3911052, 3911226, 3911401, 3911576, 3911750, 3911925, 3912099, 3912274, 3912449, 3912623, 3912798, 3912972, 3913147, 3913321, 3913496, 3913671, 3913845, 3914020, 3914194, 3914369, 3914543, 3914718, 3914892, 3915067, 3915241, 3915416, 3915591, 3915765, 3915940, 3916114, 3916289, 3916463, 3916638, 3916812, 3916987, 3917161, 3917336, 3917510, 3917685, 3917859, 3918034, 3918208, 3918383, 3918557, 3918732, 3918906, 3919081, 3919255, 3919430, 3919604, 3919779, 3919953, 3920128, 3920302, 3920477, 3920651, 3920825, 3921000, 3921174, 3921349, 3921523, 3921698, 3921872, 3922047, 3922221, 3922395, 3922570, 3922744, 3922919, 3923093, 3923268, 3923442, 3923616, 3923791, 3923965, 3924140, 3924314, 3924489, 3924663, 3924837, 3925012, 3925186, 3925361, 3925535, 3925709, 3925884, 3926058, 3926232, 3926407, 3926581, 3926756, 3926930, 3927104, 3927279, 3927453, 3927627, 3927802, 3927976, 3928150, 3928325, 3928499, 3928674, 3928848, 3929022, 3929197, 
	3929371, 3929545, 3929720, 3929894, 3930068, 3930243, 3930417, 3930591, 3930766, 3930940, 3931114, 3931288, 3931463, 3931637, 3931811, 3931986, 3932160, 3932334, 3932509, 3932683, 3932857, 3933031, 3933206, 3933380, 3933554, 3933729, 3933903, 3934077, 3934251, 3934426, 3934600, 3934774, 3934948, 3935123, 3935297, 3935471, 3935645, 3935820, 3935994, 3936168, 3936342, 3936517, 3936691, 3936865, 3937039, 3937214, 3937388, 3937562, 3937736, 3937910, 3938085, 3938259, 3938433, 3938607, 3938782, 3938956, 3939130, 3939304, 3939478, 3939653, 3939827, 3940001, 3940175, 3940349, 3940523, 3940698, 3940872, 3941046, 3941220, 3941394, 3941568, 3941743, 3941917, 3942091, 3942265, 3942439, 3942613, 3942788, 3942962, 3943136, 3943310, 3943484, 3943658, 3943832, 3944007, 3944181, 3944355, 3944529, 3944703, 3944877, 3945051, 3945225, 3945400, 3945574, 3945748, 3945922, 3946096, 3946270, 3946444, 3946618, 3946792, 3946966, 3947141, 3947315, 3947489, 3947663, 3947837, 3948011, 3948185, 3948359, 3948533, 3948707, 3948881, 3949055, 3949229, 3949403, 3949577, 3949752, 3949926, 3950100, 3950274, 3950448, 3950622, 3950796, 3950970, 3951144, 3951318, 3951492, 3967666, 3967839, 3968013, 3968187, 3968361, 3968535, 3968708, 3968882, 3969056, 3969230, 3969403, 3969577, 3969751, 3969925, 3970099, 3970272, 3970446, 3970620, 3970794, 3970967, 3971141, 3971315, 3971489, 3971662, 3971836, 3972010, 3972184, 3972357, 3972531, 3972705, 3972878, 3973052, 3973226, 3973400, 3973573, 3973747, 
	3973921, 3974094, 3974268, 3974442, 3974616, 3974789, 3974963, 3975137, 3975310, 3975484, 3975658, 3975831, 3976005, 3976179, 3976352, 3976526, 3976700, 3976873, 3977047, 3977221, 3977394, 3977568, 3977742, 3977915, 3978089, 3978263, 3978436, 3978610, 3978784, 3978957, 3979131, 3979305, 3979478, 3979652, 3979825, 3979999, 3980173, 3980346, 3980520, 3980694, 3980867, 3981041, 3981214, 3981388, 3981562, 3981735, 3981909, 3982082, 3982256, 3982430, 3982603, 3982777, 3982950, 3983124, 3983297, 3983471, 3983645, 3983818, 3983992, 3984165, 3984339, 3984512, 3984686, 3984860, 3985033, 3985207, 3985380, 3985554, 3985727, 3985901, 3986074, 3986248, 3986421, 3986595, 3986769, 3986942, 3987116, 3987289, 3987463, 3987636, 3987810, 3987983, 3988157, 3988330, 3988504, 3988677, 3988851, 3989024, 3989198, 3989371, 3989545, 3989718, 3989892, 3990065, 3990239, 3990412, 3990586, 3990759, 3990933, 3991106, 3991279, 3991453, 3991626, 3991800, 3991973, 3992147, 3992320, 3992494, 3992667, 3992841, 3993014, 3993187, 3993361, 3993534, 3993708, 3993881, 3994055, 3994228, 3994401, 3994575, 3994748, 3994922, 3995095, 3995269, 3995442, 3995615, 3995789, 3995962, 
	3996136, 3996309, 3996482, 3996656, 3996829, 3997002, 3997176, 3997349, 3997523, 3997696, 3997869, 3998043, 3998216, 3998389, 3998563, 3998736, 3998910, 3999083, 3999256, 3999430, 3999603, 3999776, 3999950, 4000123, 4000296, 4000470, 4000643, 4000816, 4000990, 4001163, 4001336, 4001510, 4001683, 4001856, 4002030, 4002203, 4002376, 4002550, 4002723, 4002896, 4003069, 4003243, 4003416, 4003589, 4003763, 4003936, 4004109, 4004283, 4004456, 4004629, 4004802, 4004976, 4005149, 4005322, 4005495, 4005669, 4005842, 4006015, 4006188, 4006362, 4006535, 4006708, 4006882, 4007055, 4007228, 4007401, 4007574, 4007748, 4007921, 4008094, 4008267, 4008441, 4008614, 4008787, 4008960, 4009134, 4009307, 4009480, 4009653, 4009826, 4010000, 4010173, 4010346, 4010519, 4010692, 4010866, 4011039, 4011212, 4011385, 4011558, 4011731, 4011905, 4012078, 4012251, 4012424, 4012597, 4012771, 4012944, 4013117, 4013290, 4013463, 4013636, 4013809, 4013983, 4014156, 4014329, 4014502, 4014675, 4014848, 4015021, 4015195, 4015368, 4015541, 4015714, 4015887, 4016060, 4016233, 4016406, 4016580, 4016753, 4016926, 4017099, 4017272, 4017445, 4017618, 4017791, 4017964, 4018137, 
	4018311, 4018484, 4018657, 4018830, 4019003, 4019176, 4019349, 4019522, 4019695, 4019868, 4020041, 4020214, 4020387, 4020560, 4020734, 4020907, 4021080, 4021253, 4021426, 4021599, 4021772, 4021945, 4022118, 4022291, 4022464, 4022637, 4022810, 4022983, 4023156, 4023329, 4023502, 4023675, 4023848, 4024021, 4024194, 4024367, 4024540, 4024713, 4024886, 4025059, 4025232, 4025405, 4025578, 4025751, 4025924, 4026097, 4026270, 4119500, 4119672, 4119844, 4120015, 4120187, 4120359, 4120530, 4120702, 4120874, 4121045, 4121217, 4121389, 4121560, 4121732, 4121904, 4122075, 4122247, 4122419, 4122590, 4122762, 4122934, 4123105, 4123277, 4123449, 4123620, 4123792, 4123963, 4124135, 4124307, 4124478, 4124650, 4124821, 4124993, 4125165, 4125336, 4125508, 4125680, 4125851, 4126023, 4126194, 4126366, 4126538, 4126709, 4126881, 4127052, 4127224, 4127395, 4127567, 4127739, 4127910, 4128082, 4128253, 4128425, 
	4128596, 4128768, 4128940, 4129111, 4129283, 4129454, 4129626, 4129797, 4129969, 4130140, 4130312, 4130483, 4130655, 4130827, 4130998, 4131170, 4131341, 4131513, 4131684, 4131856, 4132027, 4132199, 4132370, 4132542, 4132713, 4132885, 4133056, 4133228, 4133399, 4133571, 4133742, 4133914, 4134085, 4134257, 4134428, 4134600, 4134771, 4134943, 4135114, 4135286, 4135457, 4135629, 4135800, 4135971, 4136143, 4136314, 4136486, 4136657, 4136829, 4137000, 4137172, 4137343, 4137515, 4137686, 4137857, 4138029, 4138200, 4138372, 4138543, 4138715, 4138886, 4139057, 4139229, 4139400, 4139572, 4139743, 4139914, 4140086, 4140257, 4140429, 4140600, 4140771, 4140943, 4141114, 4141286, 4141457, 4141628, 4141800, 4141971, 4142143, 4142314, 4142485, 4142657, 4142828, 4142999, 4143171, 4143342, 4143513, 4143685, 4143856, 4144028, 4144199, 4144370, 4144542, 4144713, 4144884, 4145056, 4145227, 4145398, 4145570, 4145741, 4145912, 4146084, 4146255, 4146426, 4146598, 4146769, 4146940, 4147112, 4147283, 4147454, 4147625, 4147797, 4147968, 4148139, 4148311, 4148482, 4148653, 4148824, 4148996, 4149167, 4149338, 4149510, 4149681, 4149852, 4150023, 4150195, 4150366, 
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	1912017, 1912121, 1912225, 1912330, 1912434, 1912538, 1912642, 1912746, 1912851, 1912955, 1913059, 1913163, 1913268, 1913372, 1913476, 1913580, 1913685, 1913789, 1913893, 1913997, 1914101, 1914206, 1914310, 1914414, 1914518, 1914623, 1914727, 1914831, 1914935, 1915039, 1915144, 1915248, 1915352, 1915456, 1915560, 1915665, 1915769, 1915873, 1915977, 1916081, 1916186, 1916290, 1916394, 1916498, 1916602, 1916707, 1916811, 1916915, 1917019, 1917123, 1917228, 1917332, 1917436, 1917540, 1917644, 1917748, 1917853, 1917957, 1918061, 1918165, 1918269, 1918374, 1918478, 1918582, 1918686, 1918790, 1918894, 1918999, 1919103, 1919207, 1919311, 1919415, 1919519, 1919624, 1919728, 1919832, 1919936, 1920040, 1920144, 1920249, 1920353, 1920457, 1920561, 1920665, 1920769, 1920873, 1920978, 1921082, 1921186, 1921290, 1921394, 1921498, 1921603, 1921707, 1921811, 1921915, 1922019, 1922123, 1922227, 1922331, 1922436, 1922540, 1922644, 1922748, 1922852, 1922956, 1923060, 1923165, 1923269, 1923373, 1923477, 1979448, 1979552, 1979655, 1979759, 1979862, 1979966, 1980070, 1980173, 1980277, 1980380, 1980484, 1980587, 1980691, 1980794, 1980898, 1981002, 1981105, 1981209, 1981312, 1981416, 1981519, 1981623, 1981726, 1981830, 1981933, 1982037, 1982140, 1982244, 1982348, 1982451, 1982555, 1982658, 1982762, 1982865, 1982969, 1983072, 1983176, 1983279, 1983383, 1983486, 1983590, 1983693, 1983797, 1983900, 1984004, 1984107, 1984211, 1984314, 1984418, 1984522, 1984625, 1984729, 1984832, 1984936, 1985039, 1985143, 1985246, 1985350, 1985453, 1985557, 1985660, 1985764, 1985867, 1985971, 1986074, 1986178, 1986281, 1986385, 1986488, 1986592, 1986695, 1986799, 1986902, 1987005, 1987109, 1987212, 1987316, 1987419, 1987523, 1987626, 1987730, 1987833, 1987937, 1988040, 1988144, 1988247, 1988351, 1988454, 1988558, 1988661, 1988765, 1988868, 1988972, 1989075, 1989178, 1989282, 1989385, 1989489, 1989592, 1989696, 1989799, 1989903, 1990006, 1990110, 1990213, 1990317, 1990420, 1990523, 1990627, 1990730, 1990834, 1990937, 1991041, 1991144, 1991248, 1991351,
1991454, 1991558, 1991661, 
	1991765, 1991868, 1991972, 1992075, 1992179, 1992282, 1992385, 1992489, 1992592, 1992696, 1992799, 1992903, 1993006, 1993109, 1993213, 1993316, 1993420, 1993523, 1993627, 1993730, 1993833, 1993937, 1994040, 1994144, 1994247, 1994350, 1994454, 1994557, 1994661, 1994764, 1994868, 1994971, 1995074, 1995178, 1995281, 1995385, 1995488, 1995591, 1995695, 1995798, 1995902, 1996005, 1996108, 1996212, 1996315, 1996419, 1996522, 1996625, 1996729, 1996832, 1996935, 1997039, 1997142, 1997246, 1997349, 1997452, 1997556, 1997659, 1997763, 1997866, 1997969, 1998073, 1998176, 1998279, 1998383, 1998486, 1998590, 1998693, 1998796, 1998900, 1999003, 1999106, 1999210, 1999313, 1999417, 1999520, 1999623, 1999727, 1999830, 1999933, 2000037, 2000140, 2000243, 2000347, 2000450, 2000553, 2000657, 2000760, 2000864, 2000967, 2001070, 2001174, 2001277, 2001380, 2001484, 2001587, 2001690, 2001794, 2001897, 2002000, 2002104, 2002207, 2002310, 2002414, 2002517, 2002620, 2002724, 2002827, 2002930, 2003034, 2003137, 2003240, 2003344, 2003447, 2003550, 2003654, 2003757, 2003860, 2003964, 2004067, 2004170, 2004273, 2004377, 2004480, 2004583, 2004687, 2004790, 2004893, 
	2004997, 2005100, 2005203, 2005307, 2005410, 2005513, 2005616, 2005720, 2005823, 2005926, 2006030, 2006133, 2006236, 2006340, 2006443, 2006546, 2006649, 2006753, 2006856, 2006959, 2007063, 2007166, 2007269, 2007372, 2007476, 2007579, 2007682, 2007786, 2007889, 2007992, 2008095, 2008199, 2008302, 2008405, 2008509, 2008612, 2008715, 2008818, 2008922, 2009025, 2009128, 2009231, 2009335, 2009438, 2009541, 2009644, 2009748, 2009851, 2009954, 2010057, 2010161, 2010264, 2010367, 2010471, 2010574, 2010677, 2010780, 2010884, 2010987, 2011090, 2011193, 2011297, 2011400, 2011503, 2011606, 2011709, 2011813, 2011916, 2012019, 2012122, 2012226, 2012329, 2012432, 2012535, 2012639, 2012742, 2012845, 2012948, 2013052, 2013155, 2013258, 2013361, 2013464, 2013568, 2013671, 2013774, 2013877, 2013981, 2014084, 2014187, 2014290, 2014393, 2014497, 2069878, 2069981, 2070083, 2070186, 2070289, 2070391, 2070494, 2070597, 2070699, 2070802, 
	2070905, 2071007, 2071110, 2071213, 2071315, 2071418, 2071521, 2071623, 2071726, 2071829, 2071931, 2072034, 2072137, 2072239, 2072342, 2072444, 2072547, 2072650, 2072752, 2072855, 2072958, 2073060, 2073163, 2073266, 2073368, 2073471, 2073573, 2073676, 2073779, 2073881, 2073984, 2074087, 2074189, 2074292, 2074395, 2074497, 2074600, 2074702, 2074805, 2074908, 2075010, 2075113, 2075215, 2075318, 2075421, 2075523, 2075626, 2075729, 2075831, 2075934, 2076036, 2076139, 2076242, 2076344, 2076447, 2076549, 2076652, 2076755, 2076857, 2076960, 2077062, 2077165, 2077268, 2077370, 2077473, 2077575, 2077678, 2077781, 2077883, 2077986, 2078088, 2078191, 2078293, 2078396, 2078499, 2078601, 2078704, 2078806, 2078909, 2079012, 2079114, 2079217, 2079319, 2079422, 2079524, 2079627, 2079730, 2079832, 2079935, 2080037, 2080140, 2080242, 2080345, 2080447, 2080550, 2080653, 2080755, 2080858, 2080960, 2081063, 2081165, 2081268, 2081371, 2081473, 2081576, 2081678, 2081781, 2081883, 2081986, 2082088, 2082191, 2082293, 2082396, 2082499, 2082601, 2082704, 2082806, 2082909, 2083011, 2083114, 2083216, 2083319, 2083421, 2083524, 2083626, 2083729, 2083832, 2083934, 
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	2097152, 2097254, 2097357, 2097459, 2097562, 2097664, 2097766, 2097869, 2097971, 2098074, 2098176, 2098278, 2098381, 2098483, 2098586, 2098688, 2098790, 2098893, 2098995, 2099097, 2099200, 2099302, 2099405, 2099507, 2099609, 2099712, 2099814, 2099916, 2100019, 2100121, 2100224, 2100326, 2100428, 2100531, 2100633, 2100735, 2100838, 2100940, 2101042, 2101145, 2101247, 2101350, 2101452, 2101554, 2101657, 2101759, 2101861, 2101964, 2102066, 2102168, 2102271, 2102373, 2102475, 2102578, 2102680, 2102782, 2102885, 2102987, 2103090, 2103192, 2103294, 2103397, 2103499, 2103601, 2103704, 2103806, 2103908, 2104011, 2104113, 2104215, 2104318, 2104420, 2159227, 2159329, 2159431, 2159533, 2159635, 2159736, 2159838, 2159940, 2160042, 2160144, 2160245, 2160347, 2160449, 2160551, 2160653, 2160754, 2160856, 2160958, 2161060, 2161161, 2161263, 2161365, 2161467, 2161569, 2161670, 2161772, 2161874, 2161976, 2162077, 2162179, 2162281, 2162383, 
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	2253276, 2253377, 2253478, 2253579, 2253680, 2253781, 2253881, 2253982, 2254083, 2254184, 2254285, 2254386, 2254487, 2254588, 2254689, 2254789, 2254890, 2254991, 2255092, 2255193, 2255294, 2255395, 2255496, 2255597, 2255697, 2255798, 2255899, 2256000, 2256101, 2256202, 2256303, 2256403, 2256504, 2256605, 2256706, 2256807, 2256908, 2257009, 2257110, 2257210, 2257311, 2257412, 2257513, 2257614, 2257715, 2257816, 2257916, 2258017, 2258118, 2258219, 2258320, 2258421, 2258522, 2258622, 2258723, 2258824, 2258925, 2259026, 2259127, 2259227, 2259328, 2259429, 2259530, 2259631, 2259732, 2259832, 2259933, 2260034, 2260135, 2260236, 2260337, 2260437, 2260538, 2260639, 2260740, 2260841, 2260942, 2261042, 2261143, 2261244, 2261345, 2261446, 2261547, 2261647, 2261748, 2261849, 2261950, 2262051, 2262151, 2262252, 2262353, 2262454, 2262555, 2262655, 2262756, 2262857, 2262958, 2263059, 2263160, 2263260, 2263361, 2263462, 2263563, 2263664, 2263764, 2263865, 2263966, 2264067, 2264168, 2264268, 2264369, 2264470, 2264571, 2264671, 2264772, 2264873, 2264974, 2265075, 2265175, 2265276, 2265377, 2265478, 2265579, 2265679, 2265780, 2265881, 2265982, 2266082, 
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	3276064, 3276156, 3276248, 3276340, 3276432, 3276524, 3276616, 3276708, 3276800, 3276892, 3276984, 3277076, 3277168, 3277260, 3277352, 3277444, 3277536, 3277628, 3277720, 3277812, 3277904, 3277997, 3278089, 3278181, 3278273, 3278365, 3278457, 3278549, 3278641, 3278733, 3278825, 3278917, 3279009, 3279101, 3279193, 3279285, 3279377, 3279469, 3279561, 3279653, 3279745, 3279837, 3279929, 3280021, 3280113, 3280205, 3280297, 3280389, 3280481, 3280573, 3280665, 3280757, 3280849, 3280941, 3281033, 3281125, 3281217, 3281309, 3281401, 3281493, 3281585, 3281677, 3281769, 3281861, 3281953, 3282045, 3282137, 3282229, 3282321, 3282413, 3282505, 3282597, 3282689, 3282781, 3282873, 3282965, 3283057, 3283149, 3283241, 3283333, 3283425, 3283517, 3283609, 3283701, 3283793, 3283885, 3283977, 3284069, 3284161, 3284253, 3284345, 3284437, 3284529, 3284621, 3284713, 3284805, 3284897, 3284989, 3285081, 3285173, 3285265, 3285357, 3285449, 3285541, 3285633, 3285725, 3285817, 3285909, 3286001, 3286093, 3286185, 3286277, 3286369, 3286461, 3286553, 3286645, 3286737, 3286829, 3286921, 3287013, 3287104, 3287196, 3287288, 3287380, 3287472, 3287564, 3287656, 3287748, 
	3287840, 3287932, 3288024, 3288116, 3288208, 3288300, 3288392, 3288484, 3288576, 3288668, 3288760, 3288852, 3288944, 3289036, 3289128, 3289219, 3289311, 3289403, 3289495, 3289587, 3289679, 3289771, 3289863, 3289955, 3290047, 3290139, 3290231, 3290323, 3290415, 3290507, 3290599, 3290691, 3290782, 3290874, 3290966, 3291058, 3291150, 3291242, 3291334, 3291426, 3291518, 3291610, 3291702, 3291794, 3291886, 3291978, 3292069, 3292161, 3292253, 3292345, 3292437, 3292529, 3292621, 3292713, 3292805, 3292897, 3292989, 3293081, 3293173, 3293264, 3293356, 3293448, 3293540, 3293632, 3293724, 3293816, 3293908, 3294000, 3294092, 3294184, 3294275, 3294367, 3294459, 3294551, 3294643, 3294735, 3294827, 3294919, 3295011, 3295103, 3295194, 3295286, 3295378, 3295470, 3295562, 3295654, 3295746, 3295838, 3295930, 3296022, 3296113, 3296205, 3296297, 3296389, 3296481, 3296573, 3296665, 3296757, 3296849, 3296940, 3297032, 3297124, 3297216, 3297308, 3297400, 3297492, 3297584, 3297676, 3297767, 3297859, 3297951, 3298043, 3298135, 3298227, 3298319, 3298411, 3298502, 3298594, 3298686, 3298778, 3298870, 3298962, 3299054, 3299146, 3299237, 3299329, 3299421, 3299513, 
	3299605, 3299697, 3299789, 3299880, 3299972, 3300064, 3300156, 3350205, 3350296, 3350388, 3350479, 3350571, 3350662, 3350754, 3350845, 3350937, 3351028, 3351120, 3351211, 3351303, 3351394, 3351486, 3351577, 3351668, 3351760, 3351851, 3351943, 3352034, 3352126, 3352217, 3352309, 3352400, 3352492, 3352583, 3352674, 3352766, 3352857, 3352949, 3353040, 3353132, 3353223, 3353315, 3353406, 3353497, 3353589, 3353680, 3353772, 3353863, 3353955, 3354046, 3354138, 3354229, 3354320, 3354412, 3354503, 3354595, 3354686, 3354778, 3354869, 3354960, 3355052, 3355143, 3355235, 3355326, 3355418, 3355509, 3355600, 3355692, 3355783, 3355875, 3355966, 3356058, 3356149, 3356240, 3356332, 3356423, 3356515, 3356606, 3356698, 3356789, 3356880, 3356972, 3357063, 3357155, 3357246, 3357337, 3357429, 3357520, 3357612, 3357703, 3357795, 3357886, 3357977, 3358069, 3358160, 
	3358252, 3358343, 3358434, 3358526, 3358617, 3358709, 3358800, 3358891, 3358983, 3359074, 3359166, 3359257, 3359348, 3359440, 3359531, 3359623, 3359714, 3359805, 3359897, 3359988, 3360080, 3360171, 3360262, 3360354, 3360445, 3360536, 3360628, 3360719, 3360811, 3360902, 3360993, 3361085, 3361176, 3361268, 3361359, 3361450, 3361542, 3361633, 3361724, 3361816, 3361907, 3361999, 3362090, 3362181, 3362273, 3362364, 3362456, 3362547, 3362638, 3362730, 3362821, 3362912, 3363004, 3363095, 3363186, 3363278, 3363369, 3363461, 3363552, 3363643, 3363735, 3363826, 3363917, 3364009, 3364100, 3364191, 3364283, 3364374, 3364466, 3364557, 3364648, 3364740, 3364831, 3364922, 3365014, 3365105, 3365196, 3365288, 3365379, 3365470, 3365562, 3365653, 3365745, 3365836, 3365927, 3366019, 3366110, 3366201, 3366293, 3366384, 3366475, 3366567, 3366658, 3366749, 3366841, 3366932, 3367023, 3367115, 3367206, 3367297, 3367389, 3367480, 3367571, 3367663, 3367754, 3367845, 3367937, 3368028, 3368119, 3368211, 3368302, 3368393, 3368485, 3368576, 3368667, 3368759, 3368850, 3368941, 3369033, 3369124, 3369215, 3369307, 3369398, 3369489, 3369581, 3369672, 3369763, 3369854, 
	3369946, 3370037, 3370128, 3370220, 3370311, 3370402, 3370494, 3370585, 3370676, 3370768, 3370859, 3370950, 3371042, 3371133, 3371224, 3371315, 3371407, 3371498, 3371589, 3371681, 3371772, 3371863, 3371955, 3372046, 3372137, 3372228, 3372320, 3372411, 3372502, 3372594, 3372685, 3372776, 3372868, 3372959, 3373050, 3373141, 3373233, 3373324, 3373415, 3373507, 3373598, 3373689, 3373780, 3373872, 3373963, 3374054, 3374146, 3374237, 3374328, 3374419, 3374511, 3374602, 3374693, 3374785, 3374876, 3374967, 3375058, 3375150, 3375241, 3375332, 3375423, 3375515, 3375606, 3375697, 3375789, 3375880, 3375971, 3376062, 3376154, 3376245, 3376336, 3376427, 3376519, 3376610, 3376701, 3376792, 3376884, 3376975, 3377066, 3377158, 3377249, 3377340, 3377431, 3377523, 3377614, 3377705, 3377796, 3377888, 3377979, 3378070, 3378161, 3378253, 3378344, 3378435, 3378526, 3378618, 3378709, 3378800, 3378891, 3378983, 3379074, 3379165, 3379256, 3379348, 3379439, 3379530, 3379621, 3379713, 3379804, 3379895, 3379986, 3380077, 3380169, 3380260, 3380351, 3380442, 3380534, 3380625, 3380716, 3380807, 3380899, 3380990, 3381081, 3381172, 3381264, 3430696, 3430787, 3430878, 3430969, 3431060, 3431151, 3431242, 3431332, 3431423, 3431514, 3431605, 3431696, 3431787, 3431877, 3431968, 3432059, 3432150, 3432241, 3432332, 3432422, 3432513, 3432604, 3432695, 3432786, 3432877, 3432967, 3433058, 3433149, 3433240, 3433331, 3433422, 3433512, 3433603, 3433694, 3433785, 3433876, 3433967, 3434057, 3434148, 3434239, 3434330, 3434421, 3434511, 3434602, 3434693, 3434784, 3434875, 3434966, 3435056, 3435147, 3435238, 3435329, 3435420, 3435510, 3435601, 3435692, 3435783, 3435874, 3435964, 3436055, 3436146, 3436237, 3436328, 3436418, 3436509, 3436600, 3436691, 3436782, 3436872, 3436963, 3437054, 3437145, 3437236, 3437326, 3437417, 3437508, 3437599, 3437690, 3437780, 3437871, 3437962, 3438053, 3438144, 3438234, 3438325, 3438416, 3438507, 3438597, 3438688, 3438779, 3438870, 3438961, 3439051, 3439142, 3439233, 3439324, 3439415, 3439505, 3439596, 3439687, 3439778, 
	3439868, 3439959, 3440050, 3440141, 3440232, 3440322, 3440413, 3440504, 3440595, 3440685, 3440776, 3440867, 3440958, 3441048, 3441139, 3441230, 3441321, 3441412, 3441502, 3441593, 3441684, 3441775, 3441865, 3441956, 3442047, 3442138, 3442228, 3442319, 3442410, 3442501, 3442591, 3442682, 3442773, 3442864, 3442954, 3443045, 3443136, 3443227, 3443317, 3443408, 3443499, 3443590, 3443680, 3443771, 3443862, 3443953, 3444043, 3444134, 3444225, 3444316, 3444406, 3444497, 3444588, 3444679, 3444769, 3444860, 3444951, 3445042, 3445132, 3445223, 3445314, 3445404, 3445495, 3445586, 3445677, 3445767, 3445858, 3445949, 3446040, 3446130, 3446221, 3446312, 3446402, 3446493, 3446584, 3446675, 3446765, 3446856, 3446947, 3447038, 3447128, 3447219, 3447310, 3447400, 3447491, 3447582, 3447673, 3447763, 3447854, 3447945, 3448035, 3448126, 3448217, 3448308, 3448398, 3448489, 3448580, 3448670, 3448761, 3448852, 3448943, 3449033, 3449124, 3449215, 3449305, 3449396, 3449487, 3449577, 3449668, 3449759, 3449850, 3449940, 3450031, 3450122, 3450212, 3450303, 3450394, 3450484, 3450575, 3450666, 3450757, 3450847, 3450938, 3451029, 3451119, 3451210, 3451301, 3451391, 
	3451482, 3451573, 3451663, 3451754, 3451845, 3451935, 3452026, 3452117, 3452208, 3452298, 3452389, 3452480, 3452570, 3452661, 3452752, 3452842, 3452933, 3453024, 3453114, 3453205, 3453296, 3453386, 3453477, 3453568, 3453658, 3453749, 3453840, 3453930, 3454021, 3454112, 3454202, 3454293, 3454384, 3454474, 3454565, 3454656, 3454746, 3454837, 3454928, 3455018, 3455109, 3455200, 3455290, 3455381, 3455472, 3455562, 3455653, 3455744, 3455834, 3455925, 3456016, 3456106, 3456197, 3456287, 3456378, 3456469, 3456559, 3456650, 3456741, 3456831, 3456922, 3457013, 3457103, 3457194, 3457285, 3457375, 3457466, 3457557, 3457647, 3457738, 3457828, 3457919, 3458010, 3458100, 3458191, 3458282, 3458372, 3458463, 3458554, 3458644, 3458735, 3458825, 3458916, 3459007, 3459097, 3459188, 3459279, 3459369, 3459460, 3459550, 3459641, 3459732, 3459822, 3459913, 3460004, 3460094, 3460185, 3460275, 3460366, 3460457, 3460547, 3460638, 3460729, 3460819, 3460910, 3461000, 3461091, 3461182, 3461272, 3461363, 3461453, 3461544, 
};

static void BuildTrigTables()
{
//	s_SinCosTable = (float*)GlobalAlloc(GMEM_FIXED, sizeof(float)*TRIG_TABLE_SIZE);
//	s_TangentTable = (float*)GlobalAlloc(GMEM_FIXED, sizeof(float)*TRIG_TABLE_SIZE);

	float Angle = 0;
	for (int i=0;i<TRIG_TABLE_SIZE;i++)
	{
		s_SinCosTable[i]=Sine(Angle);
		s_TangentTable[i]=Tangent(Angle);

		Angle+=TRIG_TABLE_FACTOR;

	}

	// print out the tables
	debug_print("*** SINCOS TABLE ***\n");
	int x = 0;
	for (int i=0;i<TRIG_TABLE_SIZE>>4;i++)
	{
		debug_print("\t%.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff,\n", 
					s_SinCosTable[x], s_SinCosTable[x+1], s_SinCosTable[x+2], s_SinCosTable[x+3], s_SinCosTable[x+4], s_SinCosTable[x+5], s_SinCosTable[x+6], s_SinCosTable[x+7],
					s_SinCosTable[x+8], s_SinCosTable[x+9], s_SinCosTable[x+10], s_SinCosTable[x+11], s_SinCosTable[x+12], s_SinCosTable[x+13], s_SinCosTable[x+14], s_SinCosTable[x+15]);
		x+=16;
	}
	debug_print("*** TAN TABLE ***\n");
	x = 0;
	for (int i=0;i<TRIG_TABLE_SIZE>>4;i++)
	{
		debug_print("\t%.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff, %.08ff,\n", 
					s_TangentTable[x], s_TangentTable[x+1], s_TangentTable[x+2], s_TangentTable[x+3], s_TangentTable[x+4], s_TangentTable[x+5], s_TangentTable[x+6], s_TangentTable[x+7],
					s_TangentTable[x+8], s_TangentTable[x+9], s_TangentTable[x+10], s_TangentTable[x+11], s_TangentTable[x+12], s_TangentTable[x+13], s_TangentTable[x+14], s_TangentTable[x+15]);
		x+=16;
	}
	debug_print("*** END TABLES ***\n");
}

static void BuildSquareRootTable()
{
#ifdef PLATFORM_IEEE_FLOAT
  uint32 i;
  FastSqrtUnion s;

//  fast_sqrt_table = (uint32*)GlobalAlloc(GMEM_FIXED, sizeof(uint32)*0x10000);

  for (i = 0; i <= 0x7FFF; i++)
  {
    // Build a float with the bit pattern i as mantissa
    // and an exponent of 0, stored as 127
    s.i = (i << 8) | (0x7F << 23);
    s.d = (float)sqrt(s.d);

    // Take the square root then strip the first 7 bits of
    // the mantissa into the table
    fast_sqrt_table[i + 0x8000] = (s.i & 0x7FFFFF);

    // Repeat the process, this time with an exponent of 1, 
    // stored as 128
    s.i = (i << 8) | (0x80 << 23);
    s.d = (float)sqrt(s.d);

	fast_sqrt_table[i] = (s.i & 0x7FFFFF);
  }

	DebugPrint("*** fast_sqrt_table TABLE ***\n");
	for (i=0;i<0x10000>>7;i++)
	{
		DebugPrint("\t");
		for (int j=0;j<128;j++)
		{
			DebugPrint("%i, ", fast_sqrt_table[(i<<7)+j]);
		}
		DebugPrint("\n");
	}
	DebugPrint("*** end fast_sqrt_table TABLE ***\n");

#endif
}


bool gaia::InitFastMathTables()
{
	BuildTrigTables();
	BuildSquareRootTable();

	return(true);
}

void gaia::DestroyFastMathTables()
{
#ifdef PLATFORM_IEEE_FLOAT
//	GlobalFree(fast_sqrt_table);
#endif
//	GlobalFree(s_SinCosTable);
//	GlobalFree(s_TangentTable);
}

//****************************************************************************************
// end of file      ( Math.cpp )

